Purpose The purpose of this paper is to investigate the heat transfer attributes of annular fins with quarter circle profile in terms of the Biot number Bi and the radius ratio r(r). The latter corresponds to the internal radius of the tube divided by the length of the fin in question. Design/methodology/approach To this end, the governing two-dimensional (2-D) heat conduction equation in cylindrical coordinates is numerically solved via finite element analysis for different Bi (i.e., 0.1, 1 and 5) and r(r) (i.e., 0.5, 1 and 2). Findings The obtained results for the mid-plane and surface temperatures show that these profiles, which exhibit nearly r(r)-independent responses, only present one-dimensional (1-D) radially linear distributions for the case Bi = 1. For Bi = 0.1, the temperature profiles also possess a 1-D character but with a clearly defined concave pattern. Finally, for Bi = 5, a 2-D temperature field in a wide zone from the fin base is achieved with a convex pattern for the mid-plane and surface temperatures. Originality/value Exhaustive assessment of the heat transfer in annular fins with quarter circle profile in terms of different Biot numbers and radius ratios